I assume you are using a mini-displayport/thunderbolt to HDMI adapter.
Did you set the TV to take its input from the HDMI connection?
Since you don't see the Arrangment tab in your Displays preferences there's probably something physically wrong with your connections. Try clicking detect displays just to see if the computer can now sense the presence of the connection. Check your cables and make sure the mini-displayport plug is pushed firmly in. Mini-displayport plugs can be a little tricky in that you need to make sure the plug is fully seated in their socket.
Once you have an Arrangement tab, and it shows two screens, then click Gather Windows to bring the TV's Displays preferences on to your main screen if the TV is not yet showing an image. Set the proper resolution (probably 720p, 1080i, or 1080p). Set the refresh rate (probably 60Hz) if that preference is shown. You should see a picture at this point. I recommend turning off mirrored displays if it is enabled.
You may have to play with the underscan/overscan settings on your TV and the displays prefs for the TV if the picture is too small or larger for the TV screen.